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Simplifying 31x2 + -38x + 11 = 0 Reorder the terms: 11 + -38x + 31x2 = 0 Solving 11 + -38x + 31x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 31 the coefficient of the squared term: Divide each side by '31'. 0.3548387097 + -1.225806452x + x2 = 0 Move the constant term to the right: Add '-0.3548387097' to each side of the equation. 0.3548387097 + -1.225806452x + -0.3548387097 + x2 = 0 + -0.3548387097 Reorder the terms: 0.3548387097 + -0.3548387097 + -1.225806452x + x2 = 0 + -0.3548387097 Combine like terms: 0.3548387097 + -0.3548387097 = 0.0000000000 0.0000000000 + -1.225806452x + x2 = 0 + -0.3548387097 -1.225806452x + x2 = 0 + -0.3548387097 Combine like terms: 0 + -0.3548387097 = -0.3548387097 -1.225806452x + x2 = -0.3548387097 The x term is -1.225806452x. Take half its coefficient (-0.612903226). Square it (0.3756503644) and add it to both sides. Add '0.3756503644' to each side of the equation. -1.225806452x + 0.3756503644 + x2 = -0.3548387097 + 0.3756503644 Reorder the terms: 0.3756503644 + -1.225806452x + x2 = -0.3548387097 + 0.3756503644 Combine like terms: -0.3548387097 + 0.3756503644 = 0.0208116547 0.3756503644 + -1.225806452x + x2 = 0.0208116547 Factor a perfect square on the left side: (x + -0.612903226)(x + -0.612903226) = 0.0208116547 Calculate the square root of the right side: 0.144262451 Break this problem into two subproblems by setting (x + -0.612903226) equal to 0.144262451 and -0.144262451.Subproblem 1
x + -0.612903226 = 0.144262451 Simplifying x + -0.612903226 = 0.144262451 Reorder the terms: -0.612903226 + x = 0.144262451 Solving -0.612903226 + x = 0.144262451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.612903226' to each side of the equation. -0.612903226 + 0.612903226 + x = 0.144262451 + 0.612903226 Combine like terms: -0.612903226 + 0.612903226 = 0.000000000 0.000000000 + x = 0.144262451 + 0.612903226 x = 0.144262451 + 0.612903226 Combine like terms: 0.144262451 + 0.612903226 = 0.757165677 x = 0.757165677 Simplifying x = 0.757165677Subproblem 2
x + -0.612903226 = -0.144262451 Simplifying x + -0.612903226 = -0.144262451 Reorder the terms: -0.612903226 + x = -0.144262451 Solving -0.612903226 + x = -0.144262451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.612903226' to each side of the equation. -0.612903226 + 0.612903226 + x = -0.144262451 + 0.612903226 Combine like terms: -0.612903226 + 0.612903226 = 0.000000000 0.000000000 + x = -0.144262451 + 0.612903226 x = -0.144262451 + 0.612903226 Combine like terms: -0.144262451 + 0.612903226 = 0.468640775 x = 0.468640775 Simplifying x = 0.468640775Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.757165677, 0.468640775}
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